Food Goblin Supermarkets use both cashiers and baggers to serve customers at check out. During the peak hours, 8 cashiers and 6 baggers serve approximately 75 customers per hour. On average, a cashier spends 6 minutes at checkout and a bagger spends 4 minutes at bagging to serve a customer. Calculate the utilization of cashiers and their capacity cushion during a peak hour

Food Goblin Supermarkets use both cashiers and baggers to serve customers at check out. During the peak hours, 8 cashiers and 6 baggers serve approximately 75 customers per hour. On average, a cashier spends 6 minutes at checkout and a bagger spends 4 minutes at bagging to serve a customer. Calculate the utilization of cashiers and their capacity cushion during a peak hour

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 37P

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Food Goblin Supermarkets use both cashiers and baggers to serve customers at check out. During the peak hours, 8 cashiers and 6 baggers serve approximately 75 customers per hour. On average, a cashier spends 6 minutes at checkout and a bagger spends 4 minutes at bagging to serve a customer. Calculate the utilization of cashiers and their capacity cushion during a peak hour. Calculate the utilization of baggers and their capacity cushion during a peak hour. Calculate the overall average utilization of cashiers and baggers during a peak hour.
TopOil, a refiner in Indiana, serves three customers near Nashville, Tennessee and maintains consignment inventory (owned by TopOil) at each location. Currently, TopOil uses TL transportation to deliver separately to each customer. Each truck costs $800 plus $250 per stop. Thus delivering to each customer separately costs $1050 per truck. TopOil is considering aggregating deliveries to Nashville on a single truck. Demand at the large customer is 60 tons per year, demand at the medium customer is 24 tons per year, and demand at the small customer is 8 tons per year. Product cost for TopOil is $10,000 per ton and they are using a holding cost of 25 percent. Truck capacity is 12 tons. What is the optimal order quantity to each customer assuming TopOil aggregates shipments to each of the three customers on every truck that goes to Nashville?
TopOil, a refiner in Indiana, serves three customers near Nashville, Tennessee and maintains consignment inventory (owned by TopOil) at each location. Currently, TopOil uses TL transportation to deliver separately to each customer. Each truck costs $800 plus $250 per stop. Thus delivering to each customer separately costs $1050 per truck. TopOil is considering aggregating deliveries to Nashville on a single truck. Demand at the large customer is 60 tons per year, demand at the medium customer is 24 tons per year, and demand at the small customer is 8 tons per year. Product cost for TopOil is $10,000 per ton and they are using a holding cost of 25 percent. Truck capacity is 12 tons. a) What is the annual transportation and holding cost if TopOil ships a full truckoad each time a customer is running out of stock? How many days of inventory is carried at each customer under this policy.
opOil, a refiner in Indiana, serves three customers near Nashville, Tennessee and maintains consignment inventory (owned by TopOil) at each location. Currently, TopOil uses TL transportation to deliver separately to each customer. Each truck costs $800 plus $250 per stop. Thus delivering to each customer separately costs $1050 per truck. TopOil is considering aggregating deliveries to Nashville on a single truck. Demand at the large customer is 60 tons per year, demand at the medium customer is 24 tons per year, and demand at the small customer is 8 tons per year. Product cost for TopOil is $10,000 per ton and they are using a holding cost of 25 percent. Truck capacity is 12 tons. What is the optimal order quantity to each customer assuming TopOil develops a tailored aggregation policy?
A car wash offers two different types of wash services, deluxe wash and standard wash. The deluxe wash require(s) three steps: pre-wash, wash and dry. The standard wash only require(s) two steps: wash and dry. The pre-wash step has a capacity of 7 cars per hour. The wash step has a capacity of 11 cars per hour. The dry step has a capacity of 10 cars per hour. The demand for deluxe wash is 7 cars per hour and the demand for standard wash is 11 cars per hour. Instruction: Round to the nearest integer percentage. What is the implied utilization of the bottleneck resource?
Food Goblin Supermarkets use both cashiers and baggers to serve customers at check out. During the first 6 hours of each workday (Monday–Friday), 4 cashiers and 2 baggers serve approximately 20 customers per hour. A cashier and a bagger who require approximately 5 minutes at checkout and 5 minutes at bagging serve each customer. a. Calculate the utilization of both cashiers and baggers. b. Assume that both baggers and cashiers are cross-trained to perform both activities so that they can serve customers independently. Customers are now both checked and their groceries bagged by one individual. Further, assume that it takes 12 minutes for one individual to both cash out and bag each customer’s groceries. Calculate the utilization of this new group of 6 cross-trained employees.
The manager of a regional warehouse must decide on the number of loading docks to request fora new facility in order to minimize the sum of dock costs and driver-truck costs. The manager haslearned that each driver-truck combination represents a cost of $300 per day and that each dockplus loading crew represents a cost of $1,100 per day.a. How many docks should be requested if trucks arrive at the rate of three per day, each dockcan handle five trucks per day, and both rates are Poisson?
The small mail-order firm Sea’s Beginning has onephone line. An average of 60 people per hour call inorders, and it takes an average of one minute to handlea call. Time between calls and time to handle calls areexponentially distributed. If the phone line is busy, Sea’sBeginning can put up to c 2 1 people on hold. If c 2 1people are on hold, a caller gets a busy signal and calls acompetitor. Sea’s Beginning wants only 1% of all callersto get a busy signal. How many people should it be ableto put on hold, that is, what is the required value of c?
Shipping Fruit. Wollmer Distribution Company collects fruit from several small farms in the region, consolidates its collections, and then ships the fruit to a regional wholesale fruit market by truck. Having made their collections, the company has in stock 57 tons of grapes, 62 tons of peaches, and 81 tons of bananas. Wollmer owns four trucks that can transport fruit to market. Each truck has its own capacity, and Wollmer has discovered that yield losses occur at different rates depending on which fruit is carried in which truck. The truck suspension system and the efficiency of the refrigeration system seem to account for most of the losses. The following table shows the loss as a percentage: Grapes Peaches Bananas Capacity Truck 1 12% 10% 4% 40 T Truck 2 12% 14% 5% 50 T Truck 3 16% 13% 6% 55 T Truck 4 18% 17% 8% 75 T The current market prices for the three fruits are as follows: Fruit Price / Ton Grapes $ 500 Peaches 1,000 Bananas 1,750 As a logical way of loading the trucks, a…
. A refiner in city Q serves four customers near city W and maintains consignment inventory (owned by the refiner) at each location. Currently, the refiner uses TL (truckload) transportation to deliver separately to each customer. Each truck costs $(759) plus $(309) per stop. The refiner is considering aggregating deliveries to city W on a single truck. The demand of the first customer is 75 tons a year, the demand of the second customer is 30 tons per year, and the demand of the third and fourth customers is 10 tons per year. The product cost is $8,000 per ton, and it uses a holding cost of (24)%. The truck capacity is 20 tons. a. What is the optimal delivery policy to each customer if the refiner ships separately to each of them? What is the annual total inventory-related cost? b. What is the optimal delivery policy to each customer if the refiner aggregates shipments to each of the four customers on every truck that goes to city W? What is the annual total inventory-related cost?…
On average, 100 customers arrive per hour at GothamCity Bank. It takes a teller an average of two minutesto serve a customer. Interarrival and service times areexponentially distributed. The bank currently has fourtellers working. The bank manager wants to compare thefollowing two systems with regard to the average numberof customers present in the bank and the probability that acustomer will spend more than eight minutes in line.■ System 1: Each teller has his or her own line (andno moving between lines is permitted). Arrivingcustomers are equally likely to choose any teller.■ System 2: All customers wait in a single line forthe first available teller.If you were the bank manager, which system wouldyou prefer?
An automobile company assembles cars in a plant and purchases batteries from a vendor in China. The average cost of each battery is $45. The automobile company takes ownership of the batteries when they arrive at the plant. It takes exactly 12 hours to make a car in the plant and the plant assembles 200 cars per 8-hour shift (currently the plant operates one shift per day). Each car uses one battery. The company holds, on average, 8,000 Batteries in raw material inventory at the plant as a buffer. Assignment: Find the total number of batteries in the plant, on average (in work-in-process at the plant and in raw material inventory). How much are these batteries worth? How many days of supply are held in raw material inventory, on average?